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A117915 Generalized Fibonacci-like triangle. 2
1, 1, 1, 1, 2, 2, 1, 3, 3, 3, 1, 4, 4, 5, 5, 1, 5, 5, 7, 8, 8, 1, 6, 6, 9, 11, 13, 13, 1, 7, 7, 11, 14, 18, 21, 21, 1, 8, 8, 13, 27, 23, 29, 34, 34, 1, 9, 9, 15, 20, 28, 37, 47, 55, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Row sums are terms of A104161: (1, 2, 5, 10, 19, 34, 59, ...), generated by a(k) = a(k-1) + a(k-2) + n.

This is the lower triangular version of A109754 (without a row and column 0). - Ross La Haye, Apr 12 2006

LINKS

Table of n, a(n) for n=1..55.

FORMULA

Antidiagonals of the generalized Fibonacci array, rows beginning (1,1...); (1,2...); (1,3...).

EXAMPLE

Using the Fibonacci operation a(k) = a(k-1) + a(k-2), rows of the array begin (1,1...); (1,2...), (1,3...);...:

  1,  1,  2,  3,  5,  8, ...

  1,  2,  3,  5,  8, 13, ...

  1,  3,  4,  7, 11, 18, ...

  1,  4,  5,  9, 14, 23, ...

  1,  5,  6, 11, 17, 28, ...

  ...

First few rows of the triangle are:

  1;

  1,  1;

  1,  2,  2;

  1,  3,  3,  3;

  1,  4,  4,  5,  5;

  1,  5,  5,  7,  8,  8;

  1,  6,  6,  9, 11, 13, 13;

  ...

MATHEMATICA

a[n_, k_] := a[n, k] = If[k==1, 1, If[k==2, n, a[n, k-1] + a[n, k-2]]]; Table[a[n-k+1, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Aug 15 2017 *)

PROG

(Python)

from sympy.core.cache import cacheit

@cacheit

def a(n, k): return 1 if k==1 else n if k==2 else a(n, k - 1) + a(n, k - 2)

for n in range(1, 21): print [a(n - k + 1, k) for k in range(1, n + 1)] # Indranil Ghosh, Aug 19 2017

CROSSREFS

Cf. A104161.

Sequence in context: A177352 A210798 A117501 * A294453 A097094 A210870

Adjacent sequences:  A117912 A117913 A117914 * A117916 A117917 A117918

KEYWORD

nonn,tabl,changed

AUTHOR

Gary W. Adamson, Apr 02 2006

EXTENSIONS

Comment corrected by Philippe Deléham, Nov 18 2013

STATUS

approved

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Last modified December 14 05:36 EST 2019. Contains 329978 sequences. (Running on oeis4.)